All three are carrying injuries and the tournament rules only allow for one of them to be replaced if they fail to recover in time for England's opening match on 13 February.
But England chairman of selectors David Graveney is confident that they will all be fit in time for the final stages of the VB Series in Australia next month.
"Craig White will be receiving intensive treatment with the aim of having him available for the Finals of the VB Series should England qualify.
"We will also be looking to Andrew and Ashley to be fit for selection for those finals," Graveney said.
Lancashire fast bowler James Anderson has also been named in the squad.
The 21-year-old was selected after impressing during the VB series against Australia.
And his selection caps a meteoric rise during 2002, having started the winter at the ECB Academy in Adelaide before being called up to England's injury-ravaged Ashes squad.
Graveney also gave his full backing to the youngsters in the squad.
He said: "I am satisfied that the players selected in this squad represent the best mix of experience and youth that England has available to it.
"The unavailability of several key players over recent months has given us the opportunity to bring in a number of young players.
"Several of these players have responded extremely well to the challenge and we have had no hesitation in including them in the squad."
Graveney added that the players currently taking part in the VB Series, but not selected for the World Cup would be considered as injury replacements.
These include Jeremy Snape, Adam Hollioake, James Kirtley and Owais Shah.
England: Nasser Hussain (Captain), James Anderson, Ian Blackwell, Andrew Caddick, Paul Collingwood, Andy Flintoff, Ashley Giles, Steve Harmison, Matthew Hoggard, Ronnie Irani, Nick Knight, Alec Stewart, Marcus Trescothick, Michael Vaughan, Craig White